Contraction distributive property in GA

[mnb96]

Hello,
according to my book of 'Geometric Algebra' the operation of Left-Contraction for Blades has a distributive property in respect to addition. However the authors do not prove it, nor they give the smallest hint on how to derive it.

The property says that:

(\textbf{A+B})|\textbf{C}=\textbf{A}|\textbf{C}+\textbf{B}|\textbf{C}

where the symbol | denotes Left-Contraction.
Does anyone have a clue on how to prove that identity?

 

[mnb96]

Apparently the answer should be that the left contraction is constructed axiomatically by using the operations \wedge (wedge product) and \ast (scalar product), which are both bilinear. It follows, that the left-contraction must be bilinear too.